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Abstract

Numerous type-curves of dimensionless pressure versus dimensionless time have been developed in the past. They all suffer from the fact that the log-log representation has poor resolution at late time, thus the uniqueness of the poor resolution at late time, thus the uniqueness of the match is reduced.

The semi-log representation enhances the character of the pressure response but, because of the cartesian pressure pressure response but, because of the cartesian pressure scaling, the type curve technique cannot be applied. This drawback is alleviated by plotting the slope of the semi-log curve (i.e. the pressure differentiated with respect to the logarithm of time) on a log-log grid. The pressure type-curves differentiated in the same manner can thus be matched to the derivative data. The matching procedure is further improved by combining on the same plot both pressure and derivative data.

Field examples are presented showing how interpretation is enhanced by using the derivative. It is shown that the derivative sheds light on facets of pressure response that were imperceptible on pressure data alone.

The derivative can also be used to deconvolve pressures during the afterflow period of a build up, to compensate for the wellbore storage effect. Provided the wellbore storage coeffefficient is reasonably constant, the true reservoir response, which is masked at early times by wellbore storage, can be restatuted allowing interpretation of early time data. This proves especially useful in the case of heterogeneous formations with permeabilities on the high side, as demonstrated by the examples.

Introduction

The analysis of pressure data recorded during a well test has traditionally been based upon the determination of straight lines drawn on plots with specific scales. The best known is the Horner plot, which yields the most sought-after reservoir parameters (Ref. 2). Cartesian plots are used for early time data (wellbore storage plots are used for early time data (wellbore storage constant determination) or late time data (pseudo steady state interpretation). Plots of pressure versus square root or fourth root of time are used for hydraulically fractured wells. Pressure versus the inverse of square root of time is used for spherical flow etc. This straight line approach applied to specialized plots works well provided it is used during the correct flow regime, i.e. the flow regime for which the method was designed.

The type-curve matching procedure was developed to allow the identification of flow regimes. It is a global approach. The whole set of data, from very early to latest times, is matched to a type-curve which corresponds to the chosen well-reservoir model. Once a match is obtained, flow regimes are identified and specialized analysis may be applied to each and any of these regimes, yielding parameters describing the system. parameters describing the system. Type-curves require a log-log representation of the data. This representation has good resolution at early times when the pressure changes quickly, but poor resolution as later times when pressure changes are smaller.

Also, the presentation of the type-curves themselves was not conducive to obtaining a unique pressure match. (Ref. 5).

Thus the method, although theoretically sound, was often disregarded by the industry as giving unreliable and non-unique results. It was considered only when specialized analysis failed due to an apparent lack of suitable data.

On the other hand, it has always been recognised that semi-log plots exhibit much more character. Unfortunately, this representation does not allow the use of type curves because of the cartesian scale for pressure.

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